Edge of the World: When Are Manifolds Metrisable?

David Gauld ()
Additional contact information
David Gauld: University of Auckland, Department of Mathematics

Chapter Chapter 2 in Non-metrisable Manifolds, 2014, pp 21-36 from Springer

Abstract: Abstract This chapter might seem odd in that it lists a huge number of topological properties and connections between them. What it shows is that the requirement that a manifold be metrisable is extremely versatile. We list over 100 conditions each of which is equivalent to metrisability of a manifold. At one extreme, metrisability of a manifold implies that it may be embedded as a closed subset of some Euclidean space while at the other extreme knowing that every open cover of the form $$\{U_{\alpha }\ /\ {\alpha }

Keywords: Topological Space; Closed Subset; Open Cover; Dense Subset; Countable Collection (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-287-257-9_2

Ordering information: This item can be ordered from
http://www.springer.com/9789812872579

DOI: 10.1007/978-981-287-257-9_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().